Essay on the square root of 2

Essay by caseycathleenUniversity, Bachelor's June 2004

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Although it wasn't Pythagoras himself who discovered the square root of two and the changes it caused to Ancient Greek mathematics as well as the future of mathematics, his follower did and because of this he is mainly accredited. It is not believed that Pythagoras himself who revealed this mathematically changing idea because it went against his philosophy that all things are numbers. It was in reality a Pythagorean philosopher Hippasus who was able to demonstrate the irrationality of the square root of 2. The legend is that after doing so he was killed by other Pythagoreans who were scared and frantic by the thought of an irrational number. Pythagoras' follower most likely used a geometrical proof when he was first discovering the irrationality of the square root of two. This proof uses Pythagoras' theorem that in a right triangle, a2 + b2 = c2 .

If a=1, and b=1 then 2= c2.

Then c=√2 and then you must find c. However there is no rational number which satisfies this requirement. The new idea of irrational numbers changed Ancient Greek mathematics because it created two divisions including no longer just numbers (or algebra) but to geometry. It has been called a "scientific event of the highest importance." Geometry deals with distances and magnitudes and algebra focuses more on numbers. There was a crisis caused by this because in was not possible to express the quantities of irrational numbers. This gave way to future mathematicians to be able to use irrational and imaginary numbers to prove problems and discover new theories.

Two was the first irrational number to be discovered but is not the only irrational number there is. Any real number is irrational if it cannot be written as a fraction (a / b) with both a and b...